1. Chemistry 130 Chemical Equilibrium Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

2. Chemistry 130 Chemical change and equilibrium Transition state theory shows that there are always two reactions associated with a chemical change – the forward reaction and the reverse reaction. The forward reaction has a rate constant k 1 and the reverse reaction k -1 We can write a rate law for these two reactions: and the precise concentrations at equilibrium will be determined by the activation energies for the forward and reverse reactions

3. Chemistry 130 Chemical change and equilibrium We understand the relationship between the rate constant k and the activation energy; it is given by the Arrhenius equation: When the rates of the forward and reverse reactions are equal, the rates of formation and destruction of products are equal – we say that the system is at equilibrium.

4. Chemistry 130 Chemical change and equilibrium When the rates are equal, and so then

5. Chemistry 130 Chemical change and equilibrium When the rates are equal, and so then

6. Chemistry 130 Equilibrium constants As the rates are equal at equilibrium, then the K eq is a fundamental constant of the particular reaction and we call it the equilibrium constant. In general, the equilibrium constant for a reaction is Often we do not know k 1 or k -1 but we can easily measure the ratio of the two through the concentrations of the reactants and the products.

7. Chemistry 130 Equilibrium constants For a general reaction the equilibrium constant is given by In general, the equilibrium constant is written in terms of concentrations, which at their most basic are given by

8. Chemistry 130 Equilibrium constants The equilibrium constant for a reaction is useful in many ways and occurs in both thermodynamics and kinetics. The first calculation that it allows us to perform is the calculation of concentration. At 698 K, hydrogen iodide decomposes via Given

9. Chemistry 130 Equilibrium constants Rules for equilibrium constants If you reverse a reaction as written, the equilibrium constant is inverted. If you add two or more reactions together, the equilibrium constants are multiplied. If you multiply a single reaction by a number n, you raise the equilibrium constant to the power n

10. Chemistry 130 Equilibrium constants A very large or very small equilibrium constant describes a reaction that has gone to completion or one that does not perceptibly occur: For which means that the combustion of hydrogen and oxygen is essentially complete. For the reverse reaction, which implies that the reverse reaction is negligibly important.

11. Chemistry 130 Different measures of concentration For equilibria that involve gases, the concentration can be displayed in the normal manner, as However, for a perfect gas, we know the equation of state which which we can rearrange to give the concentration in terms of the pressure of the gas

12. Chemistry 130 Different measures of concentration For the decomposition of hydrogen iodide, we can therefore write the equilibrium constant either as, the equilibrium constant written in terms of concentration, or we can write it as

13. Chemistry 130 Different measures of concentration In the case of hydrogen iodide, there is no change in the number of moles of molecules involved in the equilibrium and so there is no correction term. In general, the RT correction and the relationship between and is given by the relationship where represents the change in the number of moles of gas:

14. Chemistry 130 Le Châtelier's Principle The point of equilibrium is determined by the pressure, the temperature and the numbers of particles of each type in the mixture. Although the equilibrium is dynamic, the net change at equilibrium is always the same, as long as P, T and n are constant and there is a relationship between all of these variables that dictates the position of equilibrium. The position of equilibrium is a feature of the Gibbs function and we will study this function in detail after Spring Break. If P, T, or n change, then the dynamic nature of the equilibrium ensures that the system adjusts to recover the equilibrium position. This is qualitatively summarized as Le Châtelier's Principle

15. Chemistry 130 Le Châtelier's Principle Le Châtelier's Principle states that: If a system at equilibrium is disturbed by some external influence, such as a change in temperature, pressure or composition, the system will adjust to restore the equilibrium position and minimize the effect of the external disturbance. Le Châtelier's Principle is one of the most useful qualitative concepts for the manipulation of equilibrium problems.

16. Chemistry 130 Le Châtelier's Principle: Heat An exothermic reaction is one that liberates heat to the surroundings and thereby lowers its enthalpy. We can write this evolution of heat as a product in the reaction: If we raise the temperature of an exothermic reaction, we add heat to the system and the equilibrium will move towards the reactants

17. Chemistry 130 Le Châtelier's Principle: Heat An endothermic reaction is one that absorbs heat from the surroundings and in this sense, heat is similar to a reactant: If we raise the temperature of an endothermic reaction, we add heat to the system and the equilibrium will move towards the products

18. Chemistry 130 Le Châtelier's Principle: Pressure A reaction that changes the number of moles of particles is sensitive to pressure. For the decomposition of ammonia over a tungsten catalyst, the volume of the reaction increases – we have 1 mole on the LHS and 2 moles on the RHS We can think of this as an increase in pressure as the reaction moves from the LHS to the RHS. If we increase the external pressure on this reaction, we will move the equilibrium towards the reactant.

19. Chemistry 130